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A098689 Decimal expansion of Sum_{n>=0} Fibonacci(n)/n!.

%I A098689 #18 Feb 07 2022 04:43:09
%S A098689 2,0,1,4,3,2,2,7,3,3,4,5,8,3,1,5,7,3,6,5,8,1,3,4,6,2,5,5,4,6,9,7,5,9,
%T A098689 1,3,5,6,5,9,1,1,1,4,6,9,5,8,1,1,2,4,1,8,2,1,0,8,8,4,0,3,7,6,6,7,4,2,
%U A098689 1,2,8,3,9,7,0,9,7,0,0,6,6,3,7,1,1,1,0,1,1,3,1,9,4,5,7,0,1,6,3,1,2,4,0,4,4
%N A098689 Decimal expansion of Sum_{n>=0} Fibonacci(n)/n!.
%F A098689 Equals (2/sqrt(5))*exp(1/2)*sinh(sqrt(5)/2). - _Vladeta Jovovic_, Oct 30 2004
%F A098689 Equals e * A099935. - _Amiram Eldar_, Feb 07 2022
%e A098689 2.01432273345831573658134625546975913565911146958112...
%p A098689 with(combinat): evalf(sum(fibonacci(n)/n!, n=0..infinity), 120);
%t A098689 RealDigits[ Sum[ Fibonacci[n]/n!, {n, 0, 80}], 10, 105][[1]] (* _Robert G. Wilson v_, Nov 02 2004 *)
%t A098689 (E^GoldenRatio - E^(1-GoldenRatio))/(2*GoldenRatio-1) // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 13 2013 *)
%o A098689 (PARI) sumpos(n=0, fibonacci(n)/n!) \\ _Michel Marcus_, Feb 07 2022
%Y A098689 Cf. A000045, A001113, A099935.
%K A098689 cons,nonn
%O A098689 1,1
%A A098689 Joseph Biberstine (jrbibers(AT)indiana.edu), Oct 27 2004
%E A098689 More terms from _Robert G. Wilson v_, Nov 02 2004